Cytoskeletal remodelling and slow dynamics in the living cell

Field-based dynamic light scattering microscopy: theory and numerical analysis

We present a theoretical framework for field-based dynamic light scattering microscopy based on a spectral-domain optical coherence phase microscopy (SD-OCPM) platform. SD-OCPM is an interferometric microscope capable of quantitative measurement of amplitude and phase of scattered light with high phase stability. Field-based dynamic light scattering (F-DLS) analysis allows for direct evaluation of complex-valued field autocorrelation function and measurement of localized diffusive and directional dynamic properties of biological and material samples with high spatial resolution. In order to gain insight into the information provided by F-DLS microscopy, theoretical and numerical analyses are performed to evaluate the effect of numerical aperture of the imaging optics. We demonstrate that sharp focusing of fields affects the measured diffusive and transport velocity, which leads to smaller values for the dynamic properties in the sample. An approach for accurately determining the dynamic properties of the samples is discussed.

Mechanical and structural plasticity

Excessive narrowing of the airways due to airway smooth muscle (ASM) contraction is a major cause of asthma exacerbation. ASM is therefore a direct target for many drugs used in asthma therapy. The contractile mechanism of smooth muscle is not entirely clear. A major advance in the field in the last decade was the recognition and appreciation of the unique properties of smooth muscle--mechanical and structural plasticity, characterized by the muscle's ability to rapidly alter the structure of its contractile apparatus and cytoskeleton and adapt to the mechanically dynamic environment of the lung. This article describes a possible mechanism for smooth muscle to adapt and function over a large length range by adding or subtracting contractile units in series spanning the cell length; it also describes a mechanism by which actin-myosin-actin connectivity might be influenced by thin and thick filament lengths, thus altering the muscle response to mechanical perturbation. The new knowledge is extremely useful for our understanding of ASM behavior in the lung and could provide new and more effective targets for drugs aimed at relaxing the muscle or keeping the muscle from excessive shortening in the asthmatic airways.

Myosin filaments in smooth muscle cells do not have a constant length

Myosin molecules from smooth muscle and non-muscle cells are known to self-assemble into side-polar filaments in vitro. However, the in situ mechanism of filament assembly is not clear and the question of whether there is a unique length for myosin filaments in smooth muscle is still under debate. In this study we measured the lengths of 16,587 myosin filaments in three types of smooth muscle cells using serial electron microscopy (EM). Sheep airway and pulmonary arterial smooth muscle as well as rabbit carotid arterial smooth muscle were fixed for EM and serial ultra-thin (50-60 nm) sections were obtained. Myosin filaments were traced in consecutive sections to determine their lengths. The results indicate that there is not a single length for the myosin filaments; instead there is a wide variation in lengths. The plots of observation frequency versus myosin filament length follow an exponential decay pattern. Analysis suggests that in situ assembly of myosin filaments in smooth muscle is governed by random processes of linear polymerization and de-polymerization, and that the dynamic equilibrium of these processes determines the observed length distribution.

Multicellular aggregates: a model system for tissue rheology

Morphogenetic processes involve cell flows. The mechanical response of a tissue to active forces is linked to its effective viscosity. In order to decouple this mechanical response from the complex genetic changes occurring in a developing organism, we perform rheometry experiments on multicellular aggregates, which are good models for tissues. We observe a cell softening behavior when submitting to stresses. As our technique is very sensitive, we were able to get access to the measurement of a yield point above which a creep regime is observed obtained for strains above 12%. To explain our rheological curves we propose a model for the cytoskeleton that we represent as a dynamic network of parallel springs, which will break under stress and reattach at null strain. Such a simple model is able to reproduce most of the important behavior of cells under strain. We highlight here the importance of considering cells as complex fluids whose properties will vary with time according to the history of applied stress.

Glassy dynamics, cell mechanics, and endothelial permeability

A key feature of all inflammatory processes is disruption of the vascular endothelial barrier. Such disruption is initiated in part through active contraction of the cytoskeleton of the endothelial cell (EC). Because contractile forces are propagated from cell to cell across a great many cell-cell junctions, this contractile process is strongly cooperative and highly nonlocal. We show here that the characteristic length scale of propagation is modulated by agonists and antagonists that impact permeability of the endothelial barrier. In the presence of agonists including thrombin, histamine, and H2O2, force correlation length increases, whereas in the presence of antagonists including sphingosine-1-phosphate, hepatocyte growth factor, and the rho kinase inhibitor, Y27632, force correlation length decreases. Intercellular force chains and force clusters are also evident, both of which are reminiscent of soft glassy materials approaching a glass transition.

A linear programming approach to reconstructing subcellular structures from confocal images for automated generation of representative 3D cellular models

This paper presents a novel computer vision algorithm to analyze 3D stacks of confocal images of fluorescently stained single cells. The goal of the algorithm is to create representative in silico model structures that can be imported into finite element analysis software for mechanical characterization. Segmentation of cell and nucleus boundaries is accomplished via standard thresholding methods. Using novel linear programming methods, a representative actin stress fiber network is generated by computing a linear superposition of fibers having minimum discrepancy compared with an experimental 3D confocal image. Qualitative validation is performed through analysis of seven 3D confocal image stacks of adherent vascular smooth muscle cells (VSMCs) grown in 2D culture. The presented method is able to automatically generate 3D geometries of the cell's boundary, nucleus, and representative F-actin network based on standard cell microscopy data. These geometries can be used for direct importation and implementation in structural finite element models for analysis of the mechanics of a single cell to potentially speed discoveries in the fields of regenerative medicine, mechanobiology, and drug discovery.

Cell friction

Cells sense and respond to their environment. Mechanotransduction is the process by which mechanical forces, stress, and strains are converted into biochemical signals that control cell behavior. In recent decades it has been shown that appropriate mechanical signals are essential to tissue health, but the role of friction and direct contact shearing across cell surfaces has been essentially unexplored. This, despite the obvious existence of numerous biological tissues whose express function depends on sliding contacts. In our studies on frictional interactions of corneal cells we find that the friction coefficients are on the order of mu = 0.03-0.06 for in vitro and in vivo experiments. Additionally, we observe cell death after single cycles of sliding at contact pressures estimated to be approximately 12 kPa. These experimental results suggest that frictional contact forces produce mechanical stresses and strains that are in the cellular mechanosensing ranges.

Intracellular mechanics and activity of breast cancer cells correlate with metastatic potential

Mechanics of cancer cells are directly linked to their metastatic potential, or ability to produce a secondary tumor at a distant site. Metastatic cells survive in the circulatory system in a non-adherent state, and can squeeze through barriers in the body. Such considerable structural changes in cells rely on rapid remodeling of internal structure and mechanics. While external mechanical measurements have demonstrated enhanced pliability of cancer cells with increased metastatic potential, little is known about dynamics of their interior and we expect that to change significantly in metastatic cells. We perform a comparative study, using particle-tracking to evaluate the intracellular mechanics of living epithelial breast cells with varying invasiveness. Particles in all examined cell lines exhibit super-diffusion with a scaling exponent of 1.4 at short lag times, likely related to active transport by fluctuating microtubules and their associated molecular motors. Specifics of probe-particle transport differ between the cell types, depending on the cytoskeleton network-structure and interactions with it. Our study shows that the internal microenvironment of the highly metastatic cells evaluated here is more pliable and their cytoskeleton is less dense than the poorly metastatic and benign cells. We thus reveal intracellular structure and mechanics that can support the unique function and invasive capabilities of highly metastatic cells.

Live-cell subcellular measurement of cell stiffness using a microengineered stretchable micropost array membrane

Forces are increasingly recognized as major regulators of cell structure and function, and the mechanical properties of cells, such as cell stiffness, are essential to the mechanisms by which cells sense forces, transmit them to the cell interior or to other cells, and transduce them into chemical signals that impact a spectrum of cellular responses. Here we reported a new whole-cell cell stiffness measurement technique with a subcellular spatial resolution. This technique was based on a novel cell stretching device that allowed for quantitative control and real-time measurements of mechanical stimuli and cellular biomechanical responses. Our strategy involved a microfabricated array of silicone elastomeric microposts integrated onto a stretchable elastomeric membrane. Using a computer-controlled vacuum, this micropost array membrane (mPAM) was activated to apply equibiaxial cell stretching forces to adherent cells attached on the tops of the microposts. The micropost top positions before and after mPAM stretches were recorded using fluorescence microscopy and further utilized to quantify local cell stretching forces and cell area increments. A robust computation scheme was developed and implemented for subcellular quantifications of cell stiffness using the data of local cell stretching forces and cell area increments generated from mPAM cell stretch assays. Our cell stiffness studies using the mPAM revealed strong positive correlations among cell stiffness, cellular traction force, and cell spread area, and illustrated the important functional roles of actin polymerization and myosin II-mediated cytoskeleton contractility in regulating cell stiffness. Collectively, our work reported a new approach for whole-cell stiffness measurements with a subcellular spatial resolution, which would help likely explain the complex biomechanical functions and force-sensing mechanisms of cells and design better materials for cell and tissue engineering and other applications in vivo.

Interplay between cytoskeletal stresses and cell adaptation under chronic flow

Using stress sensitive FRET sensors we have measured cytoskeletal stresses in α-actinin and the associated reorganization of the actin cytoskeleton in cells subjected to chronic shear stress. We show that long-term shear stress reduces the average actinin stress and this effect is reversible with removal of flow. The flow-induced changes in cytoskeletal stresses are found to be dynamic, involving a transient decrease in stress (phase-I), a short-term increase (3–6 min) (Phase-II), followed by a longer-term decrease that reaches a minimum in ∼20 min (Phase-III), before saturating. These changes are accompanied by reorganization of the actin cytoskeleton from parallel F-actin bundles to peripheral bundles. Blocking mechanosensitive ion channels (MSCs) with Gd³⁺ and GsMTx4 (a specific inhibitor) eliminated the changes in cytoskeletal stress and the corresponding actin reorganization, indicating that Ca²⁺ permeable MSCs participate in the signaling cascades. This study shows that shear stress induced cell adaptation is mediated via MSCs.

Cytoskeletal stiffness, friction, and fluidity of cancer cell lines with different metastatic potential

We quantified mechanical properties of cancer cells differing in metastatic potential. These cells included normal and H-ras-transformed NIH3T3 fibroblast cells, normal and oncoprotein-overexpressing MCF10A breast cancer cells, and weakly and strongly metastatic cancer cell line pairs originating from human cancers of the skin (A375P and A375SM cells), kidney (SN12C and SN12PM6 cells), prostate (PC3M and PC3MLN4 cells), and bladder (253J and 253JB5 cells). Using magnetic twisting cytometry, cytoskeletal stiffness (g') and internal friction (g″) were measured over a wide frequency range. The dependencies of g' and g″ upon frequency were used to determine the power law exponent x which is a direct measure of cytoskeletal fluidity and quantifies where the cytoskeleton resides along the spectrum of solid-like (x = 1) to fluid-like (x = 2) states. Cytoskeletal fluidity x increased following transformation by H-ras oncogene expression in NIH3T3 cells, overexpression of ErbB2 and 14-3-3-ζ in MCF10A cells, and implantation and growth of PC3M and 253J cells in the prostate and bladder, respectively. Each of these perturbations that had previously been shown to enhance cancer cell motility and invasion are shown here to shift the cytoskeleton towards a more fluid-like state. In contrast, strongly metastatic A375SM and SN12PM6 cells that disseminate by lodging in the microcirculation of peripheral organs had smaller x than did their weakly metastatic cell line pairs A375P and SN12C, respectively. Thus, enhanced hematological dissemination was associated with decreased x and a shift towards a more solid-like cytoskeleton. Taken together, these results are consistent with the notion that adaptations known to enhance metastatic ability in cancer cell lines define a spectrum of fluid-like versus solid-like states, and the position of the cancer cell within this spectrum may be a determinant of cancer progression.

Soft matter approaches to food structuring

We give an overview of the many opportunities that arise from approaching food structuring from the perspective of soft matter physics. This branch of physics employs concepts that build upon the seminal work of van der Waals, such as free volume, the mean field, and effective temperatures. All these concepts aid scientists in understanding and controlling the thermodynamics and (slow) dynamics of structured foods. We discuss the use of these concepts in four topics, which will also be addressed in a forthcoming Faraday Discussion on food structuring.

Nonequilibrium fluctuations of a remodeling in vitro cytoskeleton

Motor proteins actively contract the actin cytoskeleton of cells and thereby give rise to nonequilibrium fluctuations as well as changes in the architecture of the cytoskeleton. Here, we show, by video microrheology of a reconstituted cytoskeleton, that motors generate time-dependent nonequilibrium fluctuations, which evolve as the network is remodeled. At earlier times, the fluctuation spectrum is dominated by strong non-Gaussian fluctuations, which arise from large displacements. At later times, directed displacements are infrequent and finally disappear. We show that these effects are due to contractile coarsening of the network into large actin-myosin foci.

Optical trapping microrheology in cultured human cells

We present the microrheological study of the two close human epithelial cell lines: non-cancerous HCV29 and cancerous T24. The optical tweezers tracking was applied to extract the several seconds long trajectories of endogenous lipid granules at time step of 1μs. They were analyzed using a recently proposed equation for mean square displacement (MSD) in the case of subdiffusion influenced by an optical trap. This equation leads to an explicit form for viscoelastic moduli. The moduli of the two cell lines were found to be the same within the experimental accuracy for frequencies 10(2) - 10(5) Hz. For both cell lines subdiffusion was observed with the exponent close to 3/4, the value predicted by the theory of semiflexible polymers. For times longer than 0.1s the MSD of cancerous cells exceeds the MSD of non-cancerous cells for all values of the trapping force. Such behavior can be interpreted as a signature of the active processes and prevents the extraction of the low-frequency viscoelastic moduli for the living cells by passive microrheology.

Nonthermal ATP-dependent fluctuations contribute to the in vivo motion of chromosomal loci

Chromosomal loci jiggle in place between segregation events in prokaryotic cells and during interphase in eukaryotic nuclei. This motion seems random and is often attributed to brownian motion. However, we show here that locus dynamics in live bacteria and yeast are sensitive to metabolic activity. When ATP synthesis is inhibited, the apparent diffusion coefficient decreases, whereas the subdiffusive scaling exponent remains constant. Furthermore, the magnitude of locus motion increases more steeply with temperature in untreated cells than in ATP-depleted cells. This "superthermal" response suggests that untreated cells have an additional source of molecular agitation, beyond thermal motion, that increases sharply with temperature. Such ATP-dependent fluctuations are likely mechanical, because the heat dissipated from metabolic processes is insufficient to account for the difference in locus motion between untreated and ATP-depleted cells. Our data indicate that ATP-dependent enzymatic activity, in addition to thermal fluctuations, contributes to the molecular agitation driving random (sub)diffusive motion in the living cell.

Myelin-associated proteins block the migration of olfactory ensheathing cells: an in vitro study using single-cell tracking and traction force microscopy

Newly generated olfactory receptor axons grow from the peripheral to the central nervous system aided by olfactory ensheathing cells (OECs). Thus, OEC transplantation has emerged as a promising therapy for spinal cord injuries and for other neural diseases. However, these cells do not present a uniform population, but instead a functionally heterogeneous population that exhibits a variety of responses including adhesion, repulsion, and crossover during cell-cell and cell-matrix interactions. Some studies report that the migratory properties of OECs are compromised by inhibitory molecules and potentiated by chemical gradients. Here, we demonstrated that rodent OECs express all the components of the Nogo receptor complex and that their migration is blocked by myelin. Next, we used cell tracking and traction force microscopy to analyze OEC migration and its mechanical properties over myelin. Our data relate the decrease of traction force of OEC with lower migratory capacity over myelin, which correlates with changes in the F-actin cytoskeleton and focal adhesion distribution. Lastly, OEC traction force and migratory capacity is enhanced after cell incubation with the Nogo receptor inhibitor NEP1-40.

Duration of microbead seeding on endothelial cells significantly affects their response to magnetic excitation

Our investigation of endothelial cell rheology using optical magnetic twisting cytometry revealed that with time following incubation of ferromagnetic beads on the cells, beads were sinking into the cells and an increasing number of beads demonstrated apparent absurd negative rheological properties. In parallel, the beads' average rheological response changed considerably over time, both in magnitude and in distribution. It was hypothesized that the apparent negative rheological response was related to the above sinking process of seeded beads into the cells, resulting in an elevation of the beads' rotation axis, thus causing a reversal of the beads' lateral movement direction in response to twisting external magnetic excitation. The results suggest that microbead-based rheological characterization of cells should be interpreted with caution, while considering the time of data acquisition.

Low intensity ultrasound perturbs cytoskeleton dynamics

Therapeutic ultrasound is widely employed in clinical applications but its mechanism of action remains unclear. Here we report prompt fluidization of a cell and dramatic acceleration of its remodeling dynamics when exposed to low intensity ultrasound. These physical changes are caused by very small strains (10^-5) at ultrasonic frequencies (10⁶ Hz), but are closely analogous to those caused by relatively large strains (10^-1) at physiological frequencies (10⁰ Hz). Moreover, these changes are reminiscent of rejuvenation and aging phenomena that are well-established in certain soft inert materials. As such, we suggest cytoskeletal fluidization together with resulting acceleration of cytoskeletal remodeling events as a mechanism contributing to the salutary effects of low intensity therapeutic ultrasound.

Local motion analysis reveals impact of the dynamic cytoskeleton on intracellular subdiffusion

Intracellular transport is a complex interplay of ballistic transport along filaments and of diffusive motion, reliably delivering material and allowing for cell differentiation, migration, and proliferation. The diffusive regime, including subdiffusive, Brownian, and superdiffusive motion, is of particular interest for inferring information about the dynamics of the cytoskeleton morphology during intracellular transport. The influence of dynamic cytoskeletal states on intracellular transport are investigated in Dictyostelium discoideum cells by single particle tracking of fluorescent nanoparticles, to relate quantitative motion parameters and intracellular processes before and after cytoskeletal disruption. A local mean-square displacement (MSD) analysis separates ballistic motion phases, which we exclude here, from diffusive nanoparticle motion. In this study, we focus on intracellular subdiffusion and elucidate lag-time dependence, with particular focus on the impact of cytoskeleton compartments like microtubules and actin filaments. This method proves useful for binary motion state distributions. Experimental results are compared to simulations of a data-driven Langevin model with finite velocity correlations that captures essential statistical features of the local MSD algorithm. Specifically, the values of the mean MSD exponent and effective diffusion coefficients can be traced back to negative correlations of the motion's increments. We clearly identify both microtubules and actin filaments as the cause for intracellular subdiffusion and show that actin-microtubule cross talk exerts viscosifying effects at timescales larger than 0.2 s. Our findings might give insights into material transport and information exchange in living cells, which might facilitate gaining control over cell functions.

Rho kinase signaling pathways during stretch in primary alveolar epithelia

Alveolar epithelial cells (AECs) maintain integrity of the blood-gas barrier with actin-anchored intercellular tight junctions. Stretched type I-like AECs undergo magnitude- and frequency-dependent actin cytoskeletal remodeling into perijunctional actin rings. On the basis of published studies in human pulmonary artery endothelial cells (HPAECs), we hypothesize that RhoA activity, Rho kinase (ROCK) activity, and phosphorylation of myosin light chain II (MLC2) increase in stretched type I-like AECs in a manner that is dependent on stretch magnitude, and that RhoA, ROCK, or MLC2 activity inhibition will attenuate stretch-induced actin remodeling and preserve barrier properties. Primary type I-like AEC monolayers were stretched biaxially to create a change in surface area (ΔSA) of 12%, 25%, or 37% in a cyclic manner at 0.25 Hz for up to 60 min or left unstretched. Type I-like AECs were also treated with Rho pathway inhibitors (ML-7, Y-27632, or blebbistatin) and stained for F-actin or treated with the myosin phosphatase inhibitor calyculin-A and quantified for monolayer permeability. Counter to our hypothesis, ROCK activity and MLC2 phosphorylation decreased in type I-like AECs stretched to 25% and 37% ΔSA and did not change in monolayers stretched to 12% ΔSA. Furthermore, RhoA activity decreased in type I-like AECs stretched to 37% ΔSA. In contrast, MLC2 phosphorylation in HPAECs increased when HPAECs were stretched to 12% ΔSA but then decreased when they were stretched to 37% ΔSA, similar to type I-like AECs. Perijunctional actin rings were observed in unstretched type I-like AECs treated with the Rho pathway inhibitor blebbistatin. Myosin phosphatase inhibition increased MLC2 phosphorylation in stretched type I-like AECs but had no effect on monolayer permeability. In summary, stretch alters RhoA activity, ROCK activity, and MLC2 phosphorylation in a manner dependent on stretch magnitude and cell type.

Mechanobiology in lung epithelial cells: measurements, perturbations, and responses

Epithelial cells of the lung are located at the interface between the environment and the organism and serve many important functions including barrier protection, fluid balance, clearance of particulate, initiation of immune responses, mucus and surfactant production, and repair following injury. Because of the complex structure of the lung and its cyclic deformation during the respiratory cycle, epithelial cells are exposed to continuously varying levels of mechanical stresses. While normal lung function is maintained under these conditions, changes in mechanical stresses can have profound effects on the function of epithelial cells and therefore the function of the organ. In this review, we will describe the types of stresses and strains in the lungs, how these are transmitted, and how these may vary in human disease or animal models. Many approaches have been developed to better understand how cells sense and respond to mechanical stresses, and we will discuss these approaches and how they have been used to study lung epithelial cells in culture. Understanding how cells sense and respond to changes in mechanical stresses will contribute to our understanding of the role of lung epithelial cells during normal function and development and how their function may change in diseases such as acute lung injury, asthma, emphysema, and fibrosis.

Inhibition of Rho kinases increases directional motility of microvascular endothelial cells

Rho kinases are major regulators of actin cytoskeletal organization and cell motility. Depending on the model system, inhibitors of Rho kinases (ROCK) have been reported to increase or decrease endothelial cell migration. In the present study we investigated the effect of Rho kinase inhibitors on microvascular endothelial cell migration with a special focus on the isoform ROCK2. Migration of microvascular endothelial cells was analyzed in a wound-healing, a spheroid-on-collagen migration assay and in cells embedded in collagen-1 gels. The non-selective Rho kinase inhibitor H1152 was compared to the selective ROCK2 inhibitor SLX2119 and to siRNA knock down. Non-selective inhibition of Rho kinases decreased cell-spanning F-actin fibers, loosened cell-cell contacts visualized by VE cadherin staining, and reduced cell-matrix interactions as shown by reduced Hic-5 expression in focal contacts. Rho kinase inhibitors facilitated directed migration of endothelial cells away from spheroids on fibronectin-coated plates and in collagen-1 gels. By contrast, migration of firmly attached endothelial cells, resembling intact vessels, was not promoted by Rho kinase inhibition. Selective inhibition of ROCK2 mimicked the cytoskeletal effects of H1152 and also increased cell motility, although to a lesser extent. In summary, Rho kinase inhibition enhanced the migration and cytoskeletal restructuring preferentially in freshly attached endothelial cells. ROCK2 may be a potential target to manipulate endothelial cell migration after vessel injury.

Tensile properties of vascular smooth muscle cells: bridging vascular and cellular biomechanics

Vascular walls change their dimensions and mechanical properties adaptively in response to blood pressure. Because these responses are driven by the smooth muscle cells (SMCs) in the media, a detailed understanding of the mechanical environment of the SMCs should reveal the mechanism of the adaptation. As the mechanical properties of the media are highly heterogeneous at the microscopic level, the mechanical properties of the cells should be measured directly. The tensile properties of SMCs are, thus, important to reveal the microscopic mechanical environment in vascular tissues; their tensile properties have a close correlation with the distribution and arrangement of elements of the cytoskeletal networks, such as stress fibers and microtubules. In this review, we first introduce the experimental techniques used for tensile testing and discuss the various factors affecting the tensile properties of vascular SMCs. Cytoskeletal networks are particularly important for the mechanical properties of a cell and its mechanism of mechanotransduction; thus, the mechanical properties of cytoskeletal filaments and their effects on whole-cell mechanical properties are discussed with special attention to the balance of intracellular forces among the intracellular components that determines the force applied to each element of the cytoskeletal filaments, which is the key to revealing the mechanotransduction events regulating mechanical adaptation. Lastly, we suggest future directions to connect tissue and cell mechanics and to elucidate the mechanism of mechanical adaptation, one of the key issues of cardiovascular solid biomechanics.

Communication: Effective temperature and glassy dynamics of active matter

A systematic expansion of the many-body master equation for active matter, in which motors power configurational changes as in the cytoskeleton, is shown to yield a description of the steady state and responses in terms of an effective temperature. The effective temperature depends on the susceptibility of the motors and a Peclet number which measures their strength relative to thermal Brownian diffusion. The analytic prediction is shown to agree with previous numerical simulations and experiments. The mapping also establishes a description of aging in active matter that is also kinetically jammed.

Superdiffusion induced by a long-correlated external random force

We consider a particle immersed in a thermal reservoir and simultaneously subjected to an external random force that drives the system to a nonequilibrium situation. Starting from a Langevin equation description, we derive exact expressions for the mean-square displacement and the velocity autocorrelation function of the diffusing particle. An effective temperature is introduced to characterize the deviation from the internal equilibrium situation. Using a power-law force autocorrelation function, the mean-square displacement and the velocity autocorrelation function are analytically obtained in terms of Mittag-Leffler functions. In this case, we show that the present model exhibits a superdiffusive regime as a consequence of the competition between passive and active processes.

Focal adhesion kinase stabilizes the cytoskeleton

Focal adhesion kinase (FAK) is a central focal adhesion protein that promotes focal adhesion turnover, but the role of FAK for cell mechanical stability is unknown. We measured the mechanical properties of wild-type (FAKwt), FAK-deficient (FAK-/-), FAK-silenced (siFAK), and siControl mouse embryonic fibroblasts by magnetic tweezer, atomic force microscopy, traction microscopy, and nanoscale particle tracking microrheology. FAK-deficient cells showed lower cell stiffness, reduced adhesion strength, and increased cytoskeletal dynamics compared to wild-type cells. These observations imply a reduced stability of the cytoskeleton in FAK-deficient cells. We attribute the reduced cytoskeletal stability to rho-kinase activation in FAK-deficient cells that suppresses the formation of ordered stress fiber bundles, enhances cortical actin distribution, and reduces cell spreading. In agreement with this interpretation is that cell stiffness and cytoskeletal stability in FAK-/- cells is partially restored to wild-type level after rho-kinase inhibition with Y27632.

Active fluctuation in the cortical cytoskeleton observed by high-speed live-cell scanning probe microscopy

We investigated the dynamics of the cortical cytoskeleton in living cells by analyzing the motion of the endogenous components of the cytoskeleton using scanning probe microscopy (SPM). We performed molecular characterization of the microgranules visualized by SPM in living cells and analyzed the motion of these microgranules via particle tracking. Simultaneous SPM and epifluorescence microscopy observations showed that the microgranules recruited not only actin but also cortactin, which can bind to actin filaments. This indicates condensation of actin filaments at microgranules, leading us to identify them as "cytoskeletal microdomains". High-speed SPM observation and particle-tracking analysis showed that these cytoskeletal microdomains exhibit random walk-like diffusive fluctuations over a timescale of seconds. Inhibition of the molecular motor myosin II, which drives actin filaments, led to subdiffusive fluctuations of the microdomains. These results can be explained by longitudinal sliding of actin filaments stochastically driven by myosin II and the bending motion of the actin filaments in the absence of sliding. Analysis of the cytoskeletal microdomains thus revealed the intrinsic dynamics of the cortical cytoskeleton.

Real-time observation of flow-induced cytoskeletal stress in living cells

The mechanical stress due to shear flow has profound effects on cell proliferation, transport, gene expression, and apoptosis. The mechanisms for flow sensing and transduction are unclear, but it is postulated that fluid flow pulls upon the apical surface, and the resulting stress is eventually transmitted through the cytoskeleton to adhesion plaques on the basal surface. Here we report a direct observation of this flow-induced stress in the cytoskeleton in living cells using a parallel plate microfluidic chip with a fluorescence resonance energy transfer (FRET)-based mechanical stress sensor in actinin. The sensing cassette was genetically inserted into the cytoskeletal host protein and transfected into Madin-Darby canine kidney cells. A shear stress of 10 dyn/cm(2) resulted in a rapid increase in the FRET ratio indicating a decrease in stress across actinin with flow. The effect was reversible, and cells were able to respond to repeated stimulation and showed adaptive changes in the cytoskeleton. Flow-induced Ca(2+) elevation did not affect the response, suggesting that flow-induced changes in actinin stress are insensitive to intracellular Ca(2+) level. The reduction in FRET ratio suggests actin filaments are under normal compression in the presence of flow shear stress due to changes in cell shape, and/or actinin is not in series with actin. Treatment with cytochalasin-D that disrupts F-actin reduced prestress and the response to flow. The FRET/flow method is capable of resolving changes of stress in multiple proteins with optical spatial resolution and time resolution >1 Hz. This promises to provide insight into the force distribution and transduction in all cells.

Cadherin-dependent cell morphology in an epithelium: constructing a quantitative dynamical model

Cells in the Drosophila retina have well-defined morphologies that are attained during tissue morphogenesis. We present a computer simulation of the epithelial tissue in which the global interfacial energy between cells is minimized. Experimental data for both normal cells and mutant cells either lacking or misexpressing the adhesion protein N-cadherin can be explained by a simple model incorporating salient features of morphogenesis that include the timing of N-cadherin expression in cells and its temporal relationship to the remodeling of cell-cell contacts. The simulations reproduce the geometries of wild-type and mutant cells, distinguish features of cadherin dynamics, and emphasize the importance of adhesion protein biogenesis and its timing with respect to cell remodeling. The simulations also indicate that N-cadherin protein is recycled from inactive interfaces to active interfaces, thereby modulating adhesion strengths between cells.

Tissues are intricate, heterogeneous systems, consisting of individual cells whose shapes and relative positions are of great importance to the tissue's function, as well as to its formation during morphogenesis. To make progress in our understanding of the formation of organs, their malfunction, and their therapeutic replacement in regenerative medicine, it is crucial to elucidate the connection between shape and function. We have developed a quantitative mechanical model of an epithelial tissue, the retina of Drosophila, and compare the modeling results with experimental data. The model successfully predicts shape changes induced by different expression levels of cell-cell adhesion molecules. Furthermore, the model gives new insight into the changes a tissue undergoes during morphogenesis. Comparing simulations and experiments, we are able to accept or reject different hypotheses about morphogenetic dynamics. In this way, we can identify the time course of adhesion molecule synthesis and of cell-cell contact, as well as gain new insight into the regulation of adhesion strength. Given the prominent role of adhesion in wound healing, cancer research, and many other fields, our fundamental work introduces a novel modeling tool of universal applicability and importance.

Coordinated movements prevent jamming in an Emperor penguin huddle

For Emperor penguins (Aptenodytes forsteri), huddling is the key to survival during the Antarctic winter. Penguins in a huddle are packed so tightly that individual movements become impossible, reminiscent of a jamming transition in compacted colloids. It is crucial, however, that the huddle structure is continuously reorganized to give each penguin a chance to spend sufficient time inside the huddle, compared with time spent on the periphery. Here we show that Emperor penguins move collectively in a highly coordinated manner to ensure mobility while at the same time keeping the huddle packed. Every 30-60 seconds, all penguins make small steps that travel as a wave through the entire huddle. Over time, these small movements lead to large-scale reorganization of the huddle. Our data show that the dynamics of penguin huddling is governed by intermittency and approach to kinetic arrest in striking analogy with inert non-equilibrium systems, including soft glasses and colloids.

Generalized Langevin equation with multiplicative noise: temporal behavior of the autocorrelation functions

The temporal behavior of the mean-square displacement and the velocity autocorrelation function of a particle subjected to a periodic force in a harmonic potential well is investigated for viscoelastic media using the generalized Langevin equation. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise, by an internal Mittag-Leffler noise with a finite memory time, and by an additive external noise. It is shown that the presence of a multiplicative noise has a profound effect on the behavior of the autocorrelation functions. Particularly, for correlation functions the model predicts a crossover between two different asymptotic power-law regimes. Moreover, a dependence of the correlation function on the frequency of the external periodic forcing occurs that gives a simple criterion to discern the multiplicative noise in future experiments. It is established that additive external and internal noises cause qualitatively different dependences of the autocorrelation functions on the external forcing and also on the time lag. The influence of the memory time of the internal noise on the dynamics of the system is also discussed.

Unique slow dynamics and aging phenomena in soft glassy suspensions of multiarm star polymers

We use time-resolved rheology to elucidate the slow dynamics and aging in highly concentrated suspensions of multiarm star polymers. The linear and nonlinear rheological properties exhibit a terminal regime corresponding to a well-defined maximal relaxation time. Terminal relaxation is driven by arm relaxation which speeds up the escape of stars from their cages. The fact that the system fully relaxes and flows at long times has important consequences. The yield stress only exists in the limited range of frequencies or shear rates where solid-like behavior is observed. Aging is controlled by the total time elapsed after flow cessation and not by the time elapsed from flow cessation to the beginning of the measurement as in other glassy materials. Our results, which demonstrate the importance of particle architecture with respect to glassy dynamics, should be generic for long hairy particles.

Dynamics of the cytoskeleton: how much does water matter?

The principal constituent of the living cell is water. The role of the hydration shell and bulk H(2)O solvent is well recognized in the dynamics of isolated proteins, but the role of water in the dynamics of the integrated living cytoskeleton (CSK) remains obscure. Here we report a direct connection of dynamics of water to dynamics of the integrated CSK. The latter are known to be scale-free and to hinge upon a frequency f(0) that is roughly invariant across cell types. Although f(0) is comparable in magnitude to the rotational relaxation frequency of water (gigahertz range), the physical basis of f(0) remains unknown. Using the human airway smooth muscle cell as a model system, we show here that replacing water acutely with deuterium oxide impacts CSK dynamics in major ways, slowing CSK remodeling dynamics appreciably, and lowering f(0) by up to four orders of magnitude. Although these observations do not distinguish contributions of bulk solvent versus hydration shell, they suggest a unifying hypothesis, namely, that dynamics of integrated CSK networks are slaved in a direct fashion to fluctuations arising in intracellular water.

High- and low-frequency mechanical properties of living starfish oocytes

We studied the mechanical properties of living starfish oocytes belonging to two species, Astropecten Auranciacus and Asterina pectinifera, over a wide range of timescales. We monitored the Brownian motion of microspheres injected in the cytoplasm using laser particle-tracking (LPT) and video multiple-particle-tracking (MPT) techniques, to explore high- and low-frequency response ranges, respectively. The analysis of the mean-square-displacements (MSD) allowed us to characterize the samples on different timescales. The MSD behavior is explained by three power-law exponents: for short times (τ < 1 ms) it reflects the semiflexible behavior of the actin network; for intermediate timescales (1 ms < τ < 1 s) it is similar to that of a soft-glass material; finally for long times (τ > 1 s) it behaves mainly like a viscous medium. We computed and compared the viscoelastic moduli using a recently proposed model describing the frequency response of the cell material. The large fluctuations found in the MSD over hundreds of trajectories indicate and confirm the significant cytoplasm heterogeneity.

Squeezing and detachment of living cells

The interaction of living cells with their environment is linked to their adhesive and elastic properties. Even if the mechanics of simple lipid membranes is fairly well understood, the analysis of single cell experiments remains challenging in part because of the mechanosensory response of cells to their environment. To study the mechanical properties of living cells we have developed a tool that borrows from micropipette aspiration techniques, atomic force microscopy, and the classical Johnson-Kendall-Roberts test. We show results from a study of the adhesion properties of living cells, as well as the elastic response and relaxation. We present models that are applied throughout the different stages of an experiment, which indicate that the contribution of the different components of the cell are active at various stages of compression, retraction, and detachment. Finally, we present a model that attempts to elucidate the surprising logarithmic relaxation observed when the cell is subjected to a given deformation.

Apparent diffusive motion of centrin foci in living cells: implications for diffusion-based motion in centriole duplication

The degree to which diffusion contributes to positioning cellular structures is an open question. Here we investigate the question of whether diffusive motion of centrin granules would allow them to interact with the mother centriole. The role of centrin granules in centriole duplication remains unclear, but some proposed functions of these granules, for example, in providing pre-assembled centriole subunits, or by acting as unstable 'pre-centrioles' that need to be captured by the mother centriole (La Terra et al 2005 J. Cell Biol. 168 713-22), require the centrin foci to reach the mother. To test whether diffusive motion could permit such interactions in the necessary time scale, we measured the motion of centrin-containing foci in living human U2OS cells. We found that these centrin foci display apparently diffusive undirected motion. Using the apparent diffusion constant obtained from these measurements, we calculated the time scale required for diffusion to capture by the mother centrioles and found that it would greatly exceed the time available in the cell cycle. We conclude that mechanisms invoking centrin foci capture by the mother, whether as a pre-centriole or as a source of components to support later assembly, would require a form of directed motility of centrin foci that has not yet been observed.

Slow dynamics and internal stress relaxation in bundled cytoskeletal networks

Crosslinked and bundled actin filaments form networks that are essential for the mechanical properties of living cells. Reconstituted actin networks have been extensively studied not only as a model system for the cytoskeleton, but also to understand the interplay between microscopic structure and macroscopic viscoelastic properties of network-forming soft materials. These constitute a broad class of materials with countless applications in science and industry. So far, it has been widely assumed that reconstituted actin networks represent equilibrium structures. Here, we show that fully polymerized actin/fascin bundle networks exhibit surprising age-dependent changes in their viscoelastic properties and spontaneous dynamics, a feature strongly reminiscent of out-of-equilibrium, or glassy, soft materials. Using a combination of rheology, confocal microscopy and space-resolved dynamic light scattering, we demonstrate that actin networks build up stress during their formation and then slowly relax towards equilibrium owing to the unbinding dynamics of the crosslinking molecules.

Mesenchymal stem cell mechanics from the attached to the suspended state

Human mesenchymal stem cells (hMSCs) are therapeutically useful cells that are typically expanded in vitro on stiff substrata before reimplantation. Here we explore MSC mechanical and structural changes via atomic force microscopy and optical stretching during extended passaging, and we demonstrate that cytoskeletal organization and mechanical stiffness of attached MSC populations are strongly modulated over >15 population doublings in vitro. Cytoskeletal actin networks exhibit significant coarsening, attendant with decreasing average mechanical compliance and differentiation potential of these cells, although expression of molecular surface markers does not significantly decline. These mechanical changes are not observed in the suspended state, indicating that the changes manifest themselves as alterations in stress fiber arrangement rather than cortical cytoskeleton arrangement. Additionally, optical stretching is capable of investigating a previously unquantified structural transition: remodeling-induced stiffening over tens of minutes after adherent cells are suspended. Finally, we find that optically stretched hMSCs exhibit power-law rheology during both loading and recovery; this evidence appears to be the first to originate from a biophysical measurement technique not involving cell-probe or cell-substratum contact. Together, these quantitative assessments of attached and suspended MSCs define the extremes of the extracellular environment while probing intracellular mechanisms that contribute to cell mechanical response.

A novel small molecule target in human airway smooth muscle for potential treatment of obstructive lung diseases: a staged high-throughput biophysical screening

Background

A newly identified mechanism of smooth muscle relaxation is the interaction between the small heat shock protein 20 (HSP20) and 14-3-3 proteins. Focusing upon this class of interactions, we describe here a novel drug target screening approach for treating airflow obstruction in asthma.

Methods

Using a high-throughput fluorescence polarization (FP) assay, we screened a library of compounds that could act as small molecule modulators of HSP20 signals. We then applied two quantitative, cell-based biophysical methods to assess the functional efficacy of these molecules and rank-ordered their abilities to relax isolated human airway smooth muscle (ASM). Scaling up to the level of an intact tissue, we confirmed in a concentration-responsive manner the potency of the cell-based hit compounds.

Results

Among 58,019 compound tested, 268 compounds caused 20% or more reduction of the polarized emission in the FP assay. A small subset of these primary screen hits, belonging to two scaffolds, caused relaxation of isolated ASM cell in vitro and attenuated active force development of intact tissue ex vivo.

Conclusions

This staged biophysical screening paradigm provides proof-of-principle for high-throughput and cost-effective discovery of new small molecule therapeutic agents for obstructive lung diseases.

Stress transmission within the cell

An outstanding problem in cell biology is how cells sense mechanical forces and how those forces affect cellular functions. During past decades, it has become evident that the deformable cytoskeleton (CSK), an intracellular network of various filamentous biopolymers, provides a physical basis for transducing mechanical signals into biochemical responses. To understand how mechanical forces regulate cellular functions, it is necessary to first understand how the CSK develops mechanical stresses in response to applied forces, and how those stresses are propagated through the CSK where various signaling molecules are immobilized. New experimental techniques have been developed to quantify cytoskeletal mechanics, which together with new computational approaches have given rise to new theories and models for describing mechanics of living cells. In this article, we discuss current understanding of cell biomechanics by focusing on the biophysical mechanisms that are responsible for the development and transmission of mechanical stresses in the cell and their effect on cellular functions. We compare and contrast various theories and models of cytoskeletal mechanics, emphasizing common mechanisms that those theories are built upon, while not ignoring irreconcilable differences. We highlight most recent advances in the understanding of mechanotransduction in the cytoplasm of living cells and the central role of the cytoskeletal prestress in propagating mechanical forces along the cytoskeletal filaments to activate cytoplasmic enzymes. It is anticipated that advances in cell mechanics will help developing novel therapeutics to treat pulmonary diseases like asthma, pulmonary fibrosis, and chronic obstructive pulmonary disease.

Soft substrates promote homogeneous self-renewal of embryonic stem cells via downregulating cell-matrix tractions

Maintaining undifferentiated mouse embryonic stem cell (mESC) culture has been a major challenge as mESCs cultured in Leukemia Inhibitory Factor (LIF) conditions exhibit spontaneous differentiation, fluctuating expression of pluripotency genes, and genes of specialized cells. Here we show that, in sharp contrast to the mESCs seeded on the conventional rigid substrates, the mESCs cultured on the soft substrates that match the intrinsic stiffness of the mESCs and in the absence of exogenous LIF for 5 days, surprisingly still generated homogeneous undifferentiated colonies, maintained high levels of Oct3/4, Nanog, and Alkaline Phosphatase (AP) activities, and formed embryoid bodies and teratomas efficiently. A different line of mESCs, cultured on the soft substrates without exogenous LIF, maintained the capacity of generating homogeneous undifferentiated colonies with relatively high levels of Oct3/4 and AP activities, up to at least 15 passages, suggesting that this soft substrate approach applies to long term culture of different mESC lines. mESC colonies on these soft substrates without LIF generated low cell-matrix tractions and low stiffness. Both tractions and stiffness of the colonies increased with substrate stiffness, accompanied by downregulation of Oct3/4 expression. Our findings demonstrate that mESC self-renewal and pluripotency can be maintained homogeneously on soft substrates via the biophysical mechanism of facilitating generation of low cell-matrix tractions.

Emergence of airway smooth muscle functions related to structural malleability

The function of a complex system such as a smooth muscle cell is the result of the active interaction among molecules and molecular aggregates. Emergent macroscopic manifestations of these molecular interactions, such as the length-force relationship and its associated length adaptation, are well documented, but the molecular constituents and organization that give rise to these emergent muscle behaviors remain largely unknown. In this minireview, we describe emergent properties of airway smooth muscle that seem to have originated from inherent fragility of the cellular structures, which has been increasingly recognized as a unique and important smooth muscle attribute. We also describe molecular interactions (based on direct and indirect evidence) that may confer malleability on fragile structural elements that in turn may allow the muscle to adapt to large and frequent changes in cell dimensions. Understanding how smooth muscle works may hinge on how well we can relate molecular events to its emergent macroscopic functions.

Remodeling of integrated contractile tissues and its dependence on strain-rate amplitude

Here we investigate the origin of relaxation times governing the mechanical response of an integrated contractile tissue to imposed cyclic changes of length. When strain-rate amplitude is held constant as frequency is varied, fast events are accounted for by actomyosin cross-bridge cycling, but slow events reveal relaxation processes associated with ongoing cytoskeletal length adaptation. Although both relaxation regimes are innately nonlinear, these regimes are unified and their positions along the frequency axis are set by the imposed strain-rate amplitude.

Logarithmic superposition of force response with rapid length changes in relaxed porcine airway smooth muscle

We present a systematic quantitative analysis of power-law force relaxation and investigate logarithmic superposition of force response in relaxed porcine airway smooth muscle (ASM) strips in vitro. The term logarithmic superposition describes linear superposition on a logarithmic scale, which is equivalent to multiplication on a linear scale. Additionally, we examine whether the dynamic response of contracted and relaxed muscles is dominated by cross-bridge cycling or passive dynamics. The study shows the following main findings. For relaxed ASM, the force response to length steps of varying amplitude (0.25-4% of reference length, both lengthening and shortening) are well-fitted with power-law functions over several decades of time (10⁻² to 10³ s), and the force response after consecutive length changes is more accurately fitted assuming logarithmic superposition rather than linear superposition. Furthermore, for sinusoidal length oscillations in contracted and relaxed muscles, increasing the oscillation amplitude induces greater hysteresivity and asymmetry of force-length relationships, whereas increasing the frequency dampens hysteresivity but increases asymmetry. We conclude that logarithmic superposition is an important feature of relaxed ASM, which may facilitate a more accurate prediction of force responses in the continuous dynamic environment of the respiratory system. In addition, the single power-function response to length changes shows that the dynamics of cross-bridge cycling can be ignored in relaxed muscle. The similarity in response between relaxed and contracted states implies that the investigated passive dynamics play an important role in both states and should be taken into account.